Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n=int(input())
flag=False
x=int(math.sqrt(2*n))
flag=False
for i in range(1,x+1):
	a=2*n-(i*(i+1))
	if a>0:
		b=math.sqrt(1+4*a)
		if (b-1)/2==int((b-1)/2):
			flag=True
			print('YES')
	if flag==True:
		break
if flag==False:
	print('NO')